Unlike the total sensitivity \(t\) , the dimension \(d\)  for numerous problems was already computed in many papers in computational geometry and machine learning (in the context of PAC learning). This includes reductions and connections to similar notions such as the shattering dimension or the VC-dimension of a set. General techniques for computing the dimension of a set based on number of parameters to define a query, or number of operations that are needed to answer a query can be found in the book [1]}.
